A typical cell has a layer of negative charge on the inner surface of the cell w

Question

A typical cell has a layer of negative charge on the inner surface of the cell wall and a layer of positive charg on the wall outside surface, thus making the cell wall a capacitor.

What is the capacitance of a 50 um diameter cell with a 7.o nm thick cell wall whose dielectric constant is 9.0?

Because the cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor.

I know that the equation C=K permittivity0 A /d , but I'm not quite sure how to get the area.S=4 pi r^2,but it said we can assume the cell as a parallel-capacitor so is that S=2 pi r^2??

Explanation / Answer

Yes, use the surface area of the sphere. They just want you to ignore the fact that the inside is slightly smaller then the outside

So C = keA/d

C = (9)(8.85 X 10^-12)(4pi)(2.5 X 10^-5)^2/(7 X 10^-9)

C = 8.94 X 10^-11 F that is 89.4 pF

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